Trajectory Tracking Control Law Research Articles

An Iterative Learning-based Integrated Motion Planning and Control Method for Autonomous Patrolling of Unmanned Surface Vehicles

Abstract The minimization of maritime patrol durations and the optimization of patrol trajectories are still a prevailing challenge for autonomous navigation of Unmanned Surface Vehicles (USVs). In this paper, we propose an integrated motion planning and control method to achieve time-optimal autonomous patrol of USVs by a data-efficient iterative learning-based predictive control (ILPC) algorithm. We build the optimization problem of the algorithm by introducing a local cost and a local safe constraint set for closed-loop efficient data-driven learning. To guarantee recursive feasibility, stability and convergence properties of the optimization algorithm at each iteration, the local cost and the local constraint set are designed and update iteratively using the historical vehicle states at previous iterations as a dataset. Different from traditional optimization methods, the proposed method does not require a reference path. The cost function of the optimization method decreases monotonically and converge to obtain a time-optimal control law for trajectory planning and tracking of USVs only after several iterations. The proposed approach is validated on the robotic operation system (ROS) in typical maritime patrol scenarios. The results show that the proposed method implement a 5% reduction of patrol time, fewer cross-track errors, and smoother trajectories compared to the traditional MPC algorithm under water flow conditions. In addition, Enhancements in patrol operation efficiency of USVs are achieved by the algorithm, even under the constraints of varied patrol paths, attesting to its versatility.

IMPLEMENTATION OF FUZZY ADAPTIVE NEURONAL CONTROL APPLIED TO TRAJECTORY TRACKING OF AN AUTONOMOUS UNMANNED SURFACE VEHICLE

ABSTRACT: This article presents the hardware implementation of the fuzzy adaptive neural control law for trajectory tracking based on a simplified model of the navigation system of an autonomous unmanned surface vehicle prototype for water quality monitoring. The parameters of the simplified model are estimated. Trajectory tracking is carried out in-line by fuzzy adaptive neurons for tuning the gains of a Proportional Integral Derivative controller (PID). The stability analysis is developed. Simulations were obtained at Matlab®/Simulink for circular trajectories and the implementation in Arduino Mega boards, very good precision is obtained for the experimental results in a diving pit. Keywords: Autonomous unmanned surface vehicle, fuzzy adaptive neuronal control, trajectory tracking, implementation of a Proportional Integral Derivative controller, Arduino Mega.

Fixed-Time Trajectory Tracking Control of Fully Actuated Unmanned Surface Vessels with Error Constraints

This paper proposes a fixed-time prescribed performance control technique to address the challenge of precise trajectory tracking control for unmanned surface vessels (USVs) in the presence of external time-varying disturbances and input saturation. To begin with, a fixed-time disturbance observer is created to handle the time-varying external interference. The observer can accurately estimate and compensate for the disturbance in a fixed time, which effectively improves the robustness of the system. Furthermore, to guarantee both the transient and steady-state response of the system, we employed a specific control technology that ensures the trajectory tracking error remains within a preset bounded range. Then, combined with the fixed-time disturbance observer, the command filter, the prescribed performance control technology, and the fixed-time stability theory, a fixed-time trajectory tracking control law is designed to make the trajectory tracking error of the system converge in a fixed time. Finally, an experiment was designed to validate the suggested control scheme. The results show that under the same conditions, compared with the nonlinear controller and the finite-time controller, the absolute error tracking index of this paper is the lowest, which means that the presented control scheme has higher accuracy.

Vision-Based Adaptive Trajectory Tracking Control of Wheeled Mobile Robot With Unknown Translational External Parameters

In this article, the vision-based trajectory tracking control problem of wheeled mobile robot is addressed, and different from the traditional vision-based adaptive control methods, the case that the camera is not installed in the center of the mobile robot is considered. In this case, the visual model needs to consider the influence of unknown translational external parameters. To solve this problem, a novel adaptive vision-based trajectory tracking control method is proposed, and a two-stage switching trajectory tracking control law is designed, where the adaptive control method is used to compensate the unknown external parameters. The asymptotic convergence of tracking errors are strictly proved by applying the Lyapunov method. Simulation and experimental results show that proposed approach can effectively control the mobile robot to track the desired trajectory in the presence of unknown external translational parameters.

Trajectory Tracking Control for Quadrotor Slung Load System With Unknown Load's Linear Velocity and Cable Length

This paper addresses the trajectory tracking control problem for a quadrotor suspended load system without load's linear velocity measurement and cable length information. Firstly, the cable length is estimated by designing an immersion and invariance ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf{I\&amp;I}$</tex-math></inline-formula> )-based adaptive law. Secondly, a virtual thrust force vector is designed for the load position subsystem with the denoted auxiliary variables in the lack of load's linear velocity measurement. Then, through the cable direction subsystem and quadrotor attitude subsystem, the angular velocity input is presented to drive the real thrust input to virtual thrust input via the backstepping method. Thereafter, the uniformly boundedness of the whole closed-loop system is obtained by means of building suitable Lyapunov functions. Ultimately, numerical simulations attest to the performance of the proposed trajectory tracking control law.

A Study on General State Model of Differential Drive Wheeled Mobile Robots

This study introduces a novel approach by representing a multi-input-multi-output (MIMO) differential drive wheel mobile robot (DDWMR) using the standard state space representation for the first time. This representation facilitates the application of analysis and control system design techniques to MIMO systems. Specifically, the investigation delves into stability, controllability, observability, input-output interaction, and the relative gain array of the DDWMR model. To demonstrate the concept, the established methodology employs the conventional pole placement controller design technique to formulate a state feedback control law for trajectory tracking in the DDWMR system, utilizing both a nominal and a generalized model. The generalized model incorporates distinct parameters for the left and right motor-wheel systems, unlike the nominal model where they are assumed to be identical. Simulation results highlight that accounting for the asymmetric characteristics through the controller derived from the generalized model yields superior performance compared to the nominal model-based controller. Furthermore, the proposed model can be served as an illustrative platform for evaluating innovative MIMO control methodologies in prospective studies.

Conditioned adaptive barrier-based double integral super twisting SMC for trajectory tracking of a quadcopter and hardware in loop using IGWO algorithm

Researchers working in the field of unmanned aerial vehicles are observing rapid developments in the field, such as the use of quadrotors to grasp, manipulate, and transport objects. These advancements are made possible through sophisticated control systems, new types of actuation and sensing technologies, and a greater understanding of the aerodynamic effects and gyroscopic moment generated by the rotating blades of the quadrotor involved. Therefore, this research work proposes four novel optimized control laws, i.e., conditioned adaptive barrier-based double integral super twisting sliding mode controller (CABDIST-SMC), BF double integral SMC (BF-DISMC), BF integral SMC, and barrier function-based SMC control laws, for attitude, heading, position, and altitude trajectory tracking of the quadcopter. The non-linear model of the quadcopter is developed using the Lagrange formalism in MATLAB ODE-45 environment, including the gyroscopic moments and aerodynamic effects, and a Lyapunov stability analysis is performed to ensure the asymptotic stability of the system. A 3D-helical complex trajectory is employed to analyze the performance and consistency of the proposed optimized controllers. For performance comparison, the proposed four variants of the SMC are compared with three traditional control strategies, i.e., backstepping SMC, optimized adaptive SMC via particle swarm optimization algorithm, and improved adaptive SMC. These traditional control strategies have also been developed and tested in MATLAB-Simulink. All the controllers are optimized using the improved grey wolf optimization algorithm, and to determine the best control law, six performance indexes, i.e., mean absolute percentage error (MAPE), root mean square error (RMSE), integral square error (ISE), integral absolute error (IAE), integral time absolute error (ITAE), and integral time square error (ITSE) are used. A hardware-in-loop (HIL) test is also performed to validate the performance of the designed novel control law. The C2000 Delfino MCU F28379D launchpad is used for performing the HIL validation test. The simulated results showed that the performance of optimized CABDIST-SMC surpassed all other control laws for altitude, heading, position, and attitude trajectory tracking. It has achieved MAPE of 0.02%, RMSE of 3.9912e−5, ISE of 3.1859e−8, IAE of 7.9823e−4, ITAE of 0.0080, and ITSE of 3.1849e−7 in case of yaw angle control. The proposed control laws have successfully passed the HIL validation test, and real-time implementation of the proposed control laws indicates no significant variations compared to the simulated results.

Solid Boundary Output Feedback Control of the Stefan Problem: The Enthalpy Approach.

By taking enthalpy-an internal energy of a diffusion-type system-as the system state and expressing it in terms of the temperature profile and the phase-change interface position, the output feedback boundary control laws for a fundamentally nonlinear single-phase one-dimensional (1-D) PDE process model with moving boundaries, referred to as the Stefan problem, are developed. The control objective is tracking of the spatiotemporal temperature and temporal interface (solidification front) trajectory generated by the reference model. The external boundaries through which temperature sensing and heat flux actuation are performed are assumed to be solid. First, a full-state single-sided tracking feedback controller is presented. Then, an observer is proposed and proven to provide a stable full-state reconstruction. Finally, by combining a full-state controller with an observer, the output feedback trajectory tracking control laws are presented and the closed-loop convergence of the temperature and the interface errors proven for the single-sided and the two-sided Stefan problems. Simulation shows the exponential-like trajectory convergence attained by the implementable smooth bounded control signals.

A Simple Learning Approach for Robust Tracking Control of a Class of Dynamical Systems

This paper studies the robust tracking control problem for a class of uncertain nonlinear dynamical systems subject to unknown disturbances. A robust trajectory tracking control law is designed via a simple learning-based control strategy. In the developed design, the cost function based on the desired closed-loop error dynamics is minimized by means of gradient descent technique. A stability proof for the closed-loop nonlinear system is provided based on the pseudo-linear system theory. The learning capability of the developed robust trajectory tracking control law allows the system to mitigate the adverse effects of the uncertainties and disturbances. The numerical simulation results for a planar PPR robot are included to illustrate the effectiveness of the developed control law.

Adaptive Dynamic Programming-Based Cross-Scale Control of a Hydraulic-Driven Flexible Robotic Manipulator

This paper focuses primarily on adaptive dynamic programming (ADP)-based tracking control of the hydraulic-driven flexible robotic manipulator system (HDFRMS) with varying payloads and uncertainties via singular perturbation theory (SPT). Firstly, the dynamics is derived using a driven Jacobin matrix, which represents the coupling between the hydraulic servo-driven system and rigid–flexible manipulator established using the assumed mode method and Lagrange principle. Furthermore, the whole dynamic model of the manipulator system is decoupled into a second slow subsystem (SSS), a second fast subsystem (SFS) and a first fast subsystem (FFS). The three subsystems can describe a large range of movement, flexible vibration and electro-hydraulic servo control, respectively. Hereafter, an adaptive dynamic programming trajectory tracking control law with a critic-only policy iteration algorithm is presented in the second slow timescale, while both robust optimal control (ROC) in the second first timescale and adaptive sliding mode control (ASMC) in the first fast timescale are also designed using the Lyapunov stability theory. Finally, the numerical simulations are carried out to illustrate the rightness and robustness of the singular perturbation decomposition and proposed composite control algorithm.

Fuzzy Adaptive Control Law for Trajectory Tracking Based on a Fuzzy Adaptive Neural PID Controller of a Multi-rotor Unmanned Aerial Vehicle

Fuzzy Adaptive Control Law for Trajectory Tracking Based on a Fuzzy Adaptive Neural PID Controller of a Multi-rotor Unmanned Aerial Vehicle

Structure Design and Event-Triggered Control of a Modular Omnidirectional Mobile Chassis of Life Support Robotics

This paper addresses the problems of structure design and trajectory tracking control of a mobile chassis of life support robots. First, a novel omnidirectional mobile chassis structure is proposed, which consists of three pairs of modular wheel sets with independent drive and steering capability. This allows robots to possess omnidirectional mobility and structural reliability. Then, the trajectory tracking control law is established by combining kinematics analysis and Lyapunov theory. Furthermore, considering the requirement of life support robots to be used under network control, this paper proposes an event-triggered trajectory tracking control scheme to improve the utilization efficiency of communication resources. Finally, the effectiveness of the omnidirectional mobile chassis and the event-triggered control law designed in this paper are demonstrated by numerical simulation results.

Reinforcement learning‐based optimal trajectory tracking control of surface vessels under input saturations

AbstractThis paper develops a reinforcement learning (RL)‐based optimal trajectory tracking control scheme of surface vessels with unknown dynamics, unknown disturbances, and input saturations of surface vessels. The control scheme is designed by combining the optimal control theory, adaptive neural networks, and the RL method in a unified actor‐critic NN framework. A hyperbolic‐type penalty function of the control input is designed so as to deal with the input saturations of surface vessels. An actor‐critic NN‐based RL mechanism is established to learn the optimal trajectory tracking control law without the knowledge of the surface vessel dynamics and disturbances, where NN weights are tuned online on the basis of devised tuning laws. Theoretical analysis and simulation results prove that the proposed RL‐based optimal trajectory tracking control scheme can ensure surface vessels track the desired trajectory, while guaranteeing the boundedness of all signals in the surface vessel optimal trajectory tracking closed‐loop control system.

Event-triggered adaptive disturbance rejection for marine surface vehicles with unknown dynamics and disturbances

This article presents an event-triggered adaptive disturbance rejection scheme for marine surface vehicles with unknown model dynamics and external disturbances. The ocean environmental disturbances are expressed as a series of sinusoidal superpositions with unknown frequencies, amplitudes and phases. By incorporating the adaptive internal model principle, the disturbance rejection is transformed into the adaptive control problem. The adaptive laws and disturbance filter achieve online disturbance estimations. The adaptive neural backstepping is employed to derive the trajectory tracking control law. The event-triggering mechanism is utilized to reduce the wear and tear of thrusters. The event-triggered adaptive disturbance rejection control does not require a priori knowledge of model dynamics and can be treated as a model-free disturbance estimation and rejection scheme. It is theoretically demonstrated that the closed-loop tracking control system is semi-globally stable and the tracking error can be adjusted to be small. Illustrative results on a 1:70 scaled model CyberShip II validate the control scheme.

Tracking control for small autonomous underwater vehicles in the Trans-Atlantic Geotraverse hydrothermal field based on the modeling trajectory

• A multi-parameter high-order extended state observer is designed to estimate lumped uncertainties. • A fixed-time fault-tolerant adaptive trajectory tracking controller is presented. • The desired trajectory is constructed by interpolating the path. • The simulation topography is built according to the TAG active mound. This paper investigates the fixed-time trajectory tracking problem of small autonomous underwater vehicles (S-AUVs) in the Trans-Atlantic Geotraverse (TAG) active mound with ocean current, unknown disturbances, model uncertainties, actuator faults, and input saturations. First, the effect of the near-bottom environment of the mound on S-AUVs is analyzed in detail from three issues. Without the upper bound and gradient of lumped uncertainties, a high-order adaptive extended state observer (ESO) is designed. Then, a continuous fixed-time sliding mode manifold is applied to obtain fast convergence performance. In order to realize the fixed-time convergence of tracking errors, an adaptive fault-tolerant trajectory tracking control law with an auxiliary dynamic system (ADS) is proposed. In addition, the simulated topography of the TAG mound is constructed and the trajectory based on path points is modeled by cubic spline interpolation. The effectiveness and superiority of the proposed algorithm are validated by comprehensive simulations.

Event-Triggered Neural Sliding Mode Guaranteed Performance Control

To solve the trajectory tracking control problem for a class of nonlinear systems with time-varying parameter uncertainties and unknown control directions, this paper proposed a neural sliding mode control strategy with prescribed performance against event-triggered disturbance. First, an enhanced finite-time prescribed performance function and a compensation term containing the Hyperbolic Tangent function are introduced to design a non-singular fast terminal sliding mode (NFTSM) surface to eliminate the singularity in the terminal sliding mode control and speed up the convergence in the balanced unit-loop neighborhood. This sliding surface guarantees arbitrarily small overshoot and fast convergence speed even when triggering mistakes. Meanwhile, we utilize the Nussbaum gain function to solve the problem of unknown control directions and unknown time-varying parameters and design a self-recurrent wavelet neural network (SRWNN) to handle the uncertainty terms in the system. In addition, we use a non-periodic relative threshold event-triggered mechanism to design a new trajectory tracking control law so that the conventional time-triggered mechanism has overcome a significant resource consumption problem. Finally, we proved that all the closed-loop signals are eventually uniformly bounded according to the stability analysis theory, and the Zeno phenomenon can be eliminated. The method in this paper has a better tracking effect and faster response and can obtain better control performance with lower control energy than the traditional NFTSM method, which is verified in inverted pendulum and ball and plate system.

Cooperative Distributed Estimation and Control of Multiple Autonomous Vehicles for Range-Based Underwater Target Localization and Pursuit

We study the problem of using single or multiple cooperative autonomous vehicles, called trackers, to localize and pursue an unknown underwater moving target using measurement of the ranges between the tracker(s) and the target. At the motion planning level, each tracker is assigned a spatial–temporal (S-T) curve to track that is generated by the composition of two types of motion: along the target’s trajectory and on a path encircling the target. At the control level, we derive control laws for robust trajectory tracking and show that under mild assumptions on the convergence of the target’s state estimate provided by a suitably designed filter, the tracker converges to and remains in a desired vicinity of the target. For the case of multiple trackers, we propose an efficient distributed estimation and control (DEC) strategy for the trackers that consider explicitly the constraints on the intertracker communication network. To this end, a distributed extended Kalman filter (DEKF) and a distributed control law for cooperative S-T curve tracking are developed to cooperatively pursue and localize the target. Using this setup, all trackers converge to a specified vicinity of the target while keeping an optimal tracker-target relative geometry that maximizes the range information acquired to estimate the target’s state. The stability of the complete closed-loop DEC system is analyzed rigorously and the efficacy of the proposed strategy is illustrated with extensive computer simulations for the 2-D and 3-D cases.

Data-Driven Adaptive Disturbance Observers for Model-Free Trajectory Tracking Control of Maritime Autonomous Surface Ships.

In this article, we address the disturbance/ uncertainty estimation of maritime autonomous surface ships (MASSs) with unknown internal dynamics, unknown external disturbances, and unknown input gains. In contrast to existing disturbance observers where some prior knowledge on kinetic model parameters such as the control input gains is available in advance, reduced- and full-order data-driven adaptive disturbance observers (DADOs) are proposed for estimating unknown input gains, as well as total disturbance composed of unknown internal dynamics and external disturbances. An advantage of the proposed DADOs is that the total disturbance and input gains can be simultaneously estimated with guaranteed convergence via data-driven adaption. We apply the proposed full-order DADO for the trajectory tracking control of an MASS without kinetic modeling and present a model-free trajectory tracking control law for the ship based on the DADO and a backstepping technique. We report the simulation results to substantiate the efficacy of the proposed DADO approach to model-free trajectory tracking control of an autonomous surface ship without knowing its dynamics.

An Adaptive RBF-NMPC Architecture for Trajectory Tracking Control of Underwater Vehicles

An adaptive control algorithm based on the RBF neural network (RBFNN) and nonlinear model predictive control (NMPC) is discussed for underwater vehicle trajectory tracking control. Firstly, in the off-line phase, the improved adaptive Levenberg–Marquardt-error surface compensation (IALM-ESC) algorithm is used to establish the RBFNN prediction model. In the real-time control phase, using the characteristic that the system output will change with the external environment interference, the network parameters are adjusted by using the error between the system output and the network prediction output to adapt to the complex and uncertain working environment. This provides an accurate and real-time prediction model for model predictive control (MPC). For optimization, an improved adaptive gray wolf optimization (AGWO) algorithm is proposed to obtain the trajectory tracking control law. Finally, the tracking control performance of the proposed algorithm is verified by simulation. The simulation results show that the proposed RBF-NMPC can not only achieve the same level of real-time performance as the linear model predictive control (LMPC) but also has a superior anti-interference ability. Compared with LMPC, the tracking performance of RBF-NMPC is improved by at least 43% and 25% in the case of no interference and interference, respectively.

Improved prescribed performance anti-disturbance control for quadrotors

In this paper, an improved prescribed performance anti-disturbance control is investigated for quadrotors suffering from lumped disturbances and constrained onboard communication resources. Relative threshold event-triggered based extended state observers are respectively established in trajectory and attitude subsystems to recover the immeasurable velocity and unknown lumped disturbances with a less sampling cost, while an explicit relationship between the upper bound of estimation errors and the design parameters of event-triggered condition is derived. With the aid of estimation results, an aperiodic sampling based output feedback trajectory tracking control law is developed by inserting a relative threshold sampler into the controller-to-actuator channel, such that an enhanced robustness can be realized without involving excessive resource occupations. Additionally, a modified prescribed performance control is proposed to regulate the transient profile of trajectory tracking with an arbitrarily small overshoot and a fast convergence rate even in face of triggering error. All closed-loop signals are proved to be ultimately uniformly bounded meanwhile Zeno phenomena can be eliminated. The effectiveness of presented algorithm is validated by comparable simulations.